CN110568621A - airy beam transmission track regulation and control method based on prism phase modulation - Google Patents
airy beam transmission track regulation and control method based on prism phase modulation Download PDFInfo
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- CN110568621A CN110568621A CN201910774767.2A CN201910774767A CN110568621A CN 110568621 A CN110568621 A CN 110568621A CN 201910774767 A CN201910774767 A CN 201910774767A CN 110568621 A CN110568621 A CN 110568621A
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
- G02B27/0938—Using specific optical elements
- G02B27/0944—Diffractive optical elements, e.g. gratings, holograms
Abstract
The invention provides a method for regulating and controlling Airy beam transmission track based on prism phase modulation, which comprises the following steps: firstly, emitting a Gaussian beam by a laser, and collimating and expanding the Gaussian beam; step two, projecting the collimated and expanded Gaussian beam onto a beam splitter for light splitting; step three, the split light beams are emitted to a spatial light modulator loaded with a phase pattern in advance to carry out phase modulation; and finally, carrying out Fourier transform on the light beam passing through the cubic phase mask plate through a Fourier transform lens to obtain the Airy light beam.
Description
Technical Field
the invention relates to a method for regulating and controlling a transmission track of a Airy beam, and particularly discloses a method for regulating and controlling a transmission track of a Airy beam based on prism phase modulation.
background
The Airy beam is a non-diffraction beam and has the characteristic of transverse self-acceleration, and the transmission track of the Airy beam is similar to the parabolic trajectory under gravity acceleration. The propagation characteristic enables the Airy beam to be widely applied to various scientific fields such as particle manipulation, generation of a bent plasma channel, space-time light bullets and the like. In recent years, research on airy beams has gradually become a hot spot.
Siviloglou et al, by adding a factor related to the emission angle to the distribution function of the initial field of the Airy beam, realize the control of the transmission trajectory of the Airy beam without changing the degree of self-bending of the Airy beam. However, to precisely adjust the value of the initial emission angle requires the introduction of a complicated optical path control system.
chen et al, by decentering the centers of the fourier transform lens, the incident beam, and the spatial light modulator, introduces an initial launch angle to achieve control of the airy beam transmission trajectory. However, due to the size limitation of the spatial light modulator, the control range is greatly limited.
a large-size phase mask plate is prepared by utilizing a holographic printing technology, and the transmission track of the Airy beam is greatly regulated and controlled by a method that the phase mask plate deviates from the center of an optical axis. Although the method can regulate the Airy beam transmission track in a large range, the breadth of a large-size phase mask plate is still limited, and a mechanical control system is also introduced when the phase mask plate is required to be accurately regulated to deviate from the center position of an optical axis.
disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a method for regulating and controlling a transmission track of a blumea balsamifera beam based on prism phase modulation, and aims to solve the problem that the modulation range is limited when the track of the blumea balsamifera beam is regulated and controlled based on a spatial light modulator or a large-breadth phase mask plate.
The technical scheme adopted by the invention for solving the technical problems is as follows: a Airy beam transmission track regulation and control method based on prism phase modulation comprises the following steps:
firstly, emitting a Gaussian beam by a laser, and collimating and expanding the Gaussian beam;
step two, projecting the collimated and expanded Gaussian beam onto a beam splitter for light splitting;
Step three, the split light beams are emitted to a spatial light modulator loaded with a phase pattern in advance to carry out phase modulation;
the phase pattern in the step three is a cubic phase hologram with triangular prism phase modulation factors generated by using computer holographic technology;
and step five, obtaining a phase mask plate of the triangular prism phase modulation factor by utilizing a computer holographic technology based on the step four, wherein the phase transformation function of the triangular prism is as follows:
where n is the prism refractive index, k is the wavenumber, α is the angle of incidence, y0is the width of a right-angle edge of the triangular prism;
Step six, the distribution function of the initial light field of the Airy light beam based on the modulation in the step five is as follows: phi (s, xi ═ 0) ═ Ai(s) exp (as) exp [ +/-iks (n-1) tan alpha ] (3)
Wherein s is the normalized transverse width, ξ is the normalized propagation distance, a is the attenuation factor, and Ai represents the Airy function;
And seventhly, performing Fourier transform on the light beam passing through the cubic phase mask plate through a Fourier transform lens to obtain the Airy light beam.
The light field function distribution after Fourier lens transformation in the step eight and the step seven is as follows:
φ(ζ，s)＝Ai[s-(ζ/2)2+i(a±i(n-1)tanα)ζ]exp[(a±i(n-1)tanα)s-((a±i(n-1)tanα)ζ2/2)-i(ζ3/12)+i((a±i(n-1)tanα)2ζ/2)+i(sξ/2)] (4)
Further, after the eighth step is completed, the airy beam is received by the camera.
The utility model provides a light beam transmission orbit regulation and control device in chinese mugwort based on prism phase modulation which characterized in that: the device comprises a laser used for emitting Gaussian beams, a collimation and beam expansion lens used for collimating and expanding the Gaussian beams, a beam splitter used for splitting the beams after being collimated and expanded, a spatial light modulator used for carrying out phase modulation on the split beams, and a Fourier transform lens used for carrying out Fourier transform on the beams after being phase modulated to obtain Airy beams.
further, the device also comprises a camera for receiving the Airy light beam.
The beneficial effects of the invention are mainly shown in the following aspects: the invention regulates and controls the transmission track of the Airy beam by introducing the phase modulation factor of the triangular prism, overcomes the limitation of the breadth size of the phase mask plate on the regulation and control range, and has higher regulation and control precision because the transmission track of the Airy beam is accurately controlled by two parameters of the triangular prism.
Drawings
FIG. 1 is a schematic illustration of the phase modulation factor sign of the right triangular prism of the present invention;
FIG. 2 is a schematic diagram of a control device for generating Airy beams according to the present invention;
Fig. 3 is a schematic diagram of a phase mask plate and a transmission rail when a refractive index n of a prism is 1.8 and an apex angle α of the prism is 30 ° in the present invention;
The labels in the figure are: 1. the device comprises a laser, 2, a collimation beam expander, 3, a beam splitter, 4, a spatial light modulator, 5, a Fourier transform lens, 6 and a camera.
Detailed Description
the embodiments of the present invention are described in detail with reference to the accompanying drawings, and the embodiments and specific operations of the embodiments are provided on the premise of the technical solution of the present invention, but the scope of the present invention is not limited to the following embodiments.
According to the attached drawings, the Airy beam transmission track regulation and control method based on prism phase modulation comprises the following steps:
Firstly, emitting a Gaussian beam by a laser, and collimating and expanding the Gaussian beam;
Step two, projecting the collimated and expanded Gaussian beam onto a beam splitter for light splitting;
step three, the split light beams are emitted to a spatial light modulator loaded with a phase pattern in advance to carry out phase modulation;
the phase pattern in the step three is a cubic phase hologram with triangular prism phase modulation factors generated by using computer holographic technology;
And step five, obtaining a phase mask plate of the triangular prism phase modulation factor by utilizing a computer holographic technology based on the step four, wherein the phase transformation function of the triangular prism is as follows:
Where n is the prism refractive index, k is the wavenumber, α is the angle of incidence, y0is the width of a right-angle edge of the triangular prism;
step six, the distribution function of the initial light field of the Airy light beam based on the modulation in the step five is as follows:
φ(s，ξ＝0)＝Ai(s)exp(as)exp[±iks(n-1)tanα] (3)
Where s is the normalized lateral width, ζ is the normalized propagation distance, a is the attenuation factor, and Ai represents the Airy function;
and seventhly, performing Fourier transform on the light beam passing through the cubic phase mask plate through a Fourier transform lens to obtain the Airy light beam.
The light field function distribution after Fourier lens transformation in the step eight and the step seven is as follows:
φ(ξ，s)＝Ai[s-(ξ/2)2+i(a±i(n-1)tana)ξ]exp[(n±i(n-1)tanα)s-((a±i(n-1)tanα)ξ2/2)-i(ζ3/12)+i((a±i(n-1)tanα)2ξ/2)+i(sξ/2)] (4)
wherein the sign of i (n-1) tan α depends on the sign of the triangular prism wedge angle slope (see FIG. 1); the phase modulation factor of the triangular prism indicates that the regulation and control function of the triangular prism is a linear regulation and control function. The regulation of the airy beam transmission trajectory by the prism in the spatial domain corresponds to the phase shift of the airy light field in the frequency domain space.
Further, after the eighth step is completed, the airy beam is received by the camera.
the utility model provides a light beam transmission orbit regulation and control device in chinese mugwort based on prism phase modulation which characterized in that: the device comprises a laser 1 for emitting Gaussian beams, a collimation and beam expansion lens 2 for collimating and expanding the Gaussian beams, a beam splitter 3 for splitting the beams after being collimated and expanded, a spatial light modulator 4 for phase modulating the split beams, and a Fourier transform lens 5 for Fourier transforming the phase modulated beams to obtain Airy beams, wherein the beam splitter is a beam splitting prism.
Further, a camera 6 for receiving the airy beam is included.
The experimental implementation process of the invention is as follows:
1. According to the principle of calculating holography, obtaining an Airy beam transmission track under a known certain prism parameter through simulation, and obtaining a corresponding holographic phase mask plate by changing the parameter setting of a prism;
2. The phase mask plate generated in the implementation process 1 is loaded on a spatial light modulator (4) in an experimental device (fig. 2), and an airy beam with a transmission track capable of being freely regulated and controlled can be obtained.
The implementation mode is as follows: in the following, a mask with a size of 512 × 512 is taken as an example, and a cubic phase mask under a known modulation parameter and an airy beam transmission track under a corresponding parameter are given for a laser with an operating wavelength of 632.8 nm.
The method comprises the steps of selecting the attenuation factor Airy beam with a equal to 0.1, setting the refractive index of a prism to be 1.8, setting the vertex angle alpha of the prism to be 30 degrees, and setting the phase modulation factor sign of the prism to be a plus sign. By using the formula (3) given above and combining the principle of computer-generated holography, a cubic phase mask (fig. 3a) under corresponding parameters is obtained. The experimental setup shown in fig. 2 was followed by placing the optical elements and loading the phase mask shown in fig. 3a onto the spatial light modulator to produce airy beams with corresponding transmission trajectories (fig. 3 c). Fig. 3(b) and (d) are phase mask plate and airy beam transmission trace diagrams corresponding to the situation that the triangular prism phase modulation factor takes a negative sign under the same parameters.
The holographic mask plate generated by utilizing the computer-generated holographic technology breaks through the limitation of the value range of the prism related parameters in the actual situation, and greatly improves the regulation and control range of the light beam transmission track.
the above-mentioned embodiment is only one specific implementation manner of the present invention, and is not to be construed as limiting the scope of the present invention.
The transmission track of the Airy light beam is regulated and controlled by introducing the phase modulation factor of the triangular prism, so that the limitation of the breadth size of a phase mask plate on the regulation and control range is overcome, and the regulation and control precision of the transmission track of the Airy light beam is accurately controlled by two parameters of the triangular prism is higher.
it should also be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element. The above-mentioned embodiment is only one specific implementation manner of the present invention, and is not to be construed as limiting the scope of the present invention. It will be apparent to those skilled in the art that various changes and modifications can be made in the details of the embodiments set forth in the disclosure without departing from the spirit of the disclosure, and these are intended to be included within the scope of the disclosure.
Claims (4)
1. A Airy beam transmission track regulation and control method based on prism phase modulation is characterized in that: the method comprises the following steps:
firstly, emitting a Gaussian beam by a laser, and collimating and expanding the Gaussian beam;
step two, projecting the collimated and expanded Gaussian beam onto a beam splitter for light splitting;
step three, the split light beams are emitted to a spatial light modulator loaded with a phase pattern in advance to carry out phase modulation;
The phase pattern in the step three is a cubic phase hologram with triangular prism phase modulation factors generated by using computer holographic technology;
and step five, obtaining a phase mask plate of the triangular prism phase modulation factor by utilizing a computer holographic technology based on the step four, wherein the phase transformation function of the triangular prism is as follows:
where n is the prism refractive index, k is the wavenumber, α is the angle of incidence, y0Is the width of a right-angle edge of the triangular prism;
Step six, the distribution function of the initial light field of the Airy light beam based on the modulation in the step five is as follows:
φ(s，ξ＝0)＝Ai(s)exp(as)exp[±iks(n-1)tanα] (3)
Wherein s is the normalized transverse width, ξ is the normalized propagation distance, a is the attenuation factor, and Ai represents the Airy function;
And seventhly, performing Fourier transform on the light beam passing through the cubic phase mask plate through a Fourier transform lens to obtain the Airy light beam.
The light field function distribution after Fourier lens transformation in the step eight and the step seven is as follows:
φ(ξ，s)＝Ai[s-(ξ/2)2+i(a±i(n-1)tanα)ξ]exp[(a±i(n-1)tanα)s-((a±i(n-1)tanα)ξ2/2)-i(ξ3/12)+i((a±i(n-1)tanα)2ξ/2)+i(sξ/2)] (4)
2. The method for regulating the Airy beam transmission track based on prism phase modulation according to claim 1, wherein: and after the step eight is finished, receiving the Airy light beam through the camera.
3. the airy beam transmission track regulating device based on prism phase modulation according to claim 1, wherein: the device comprises a laser used for emitting Gaussian beams, a collimation and beam expansion lens used for collimating and expanding the Gaussian beams, a beam splitter used for splitting the beams after being collimated and expanded, a spatial light modulator used for carrying out phase modulation on the split beams, and a Fourier transform lens used for carrying out Fourier transform on the beams after being phase modulated to obtain Airy beams.
4. The device for regulating the transmission track of the Airy beams based on prism phase modulation according to claim 3, further comprising a camera for receiving the Airy beams.
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| CN111092653A (en) * | 2019-12-18 | 2020-05-01 | 南京信息工程大学 | Device for realizing dual-polarization Airy obstacle-detouring signal transmission based on single SLM space partition |
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Application publication date: 20191213 |